6a^2-15a=11a+22

Solution for 6a^2-15a=11a+22 equation:

6a^2-15a=11a+22

We move all terms to the left:

6a^2-15a-(11a+22)=0

We get rid of parentheses

6a^2-15a-11a-22=0

We add all the numbers together, and all the variables

6a^2-26a-22=0

a = 6; b = -26; c = -22;
Δ = b2-4ac
Δ = -262-4·6·(-22)
Δ = 1204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{301}}{2*6}=\frac{26-2\sqrt{301}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{301}}{2*6}=\frac{26+2\sqrt{301}}{12}
$